Canonical Brownian Motion on the Diffeomorphism Group of the Circle

For infinitesimal data given on the group of diffeomorphism of the circle with respect to the metric H^3/2, the associated Brownian motion has been constructed by Malliavin (C.R. Acad. Sci. Parist.329 (1999), 325-329). In this work, we shall give another approach and prove the invariance of heat measures under the adjoint action of S¹.